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Mathematical Problems in Engineering
Volume 2008, Article ID 935390, 14 pages
http://dx.doi.org/10.1155/2008/935390
Research Article

On the Existence of Bright Solitons in Cubic-Quintic Nonlinear Schrödinger Equation with Inhomogeneous Nonlinearity

1Departamento de Matemáticas, E.T.S de Ingenieros Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
2Instituto de Matemática Aplicada a la Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain

Received 21 April 2008; Revised 3 July 2008; Accepted 4 July 2008

Academic Editor: Mehrdad Massoudi

Copyright © 2008 Juan Belmonte-Beitia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give a proof of the existence of stationary bright soliton solutions of the cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity. By using bifurcation theory, we prove that the norm of the positive solution goes to zero as the parameter , called chemical potential in the Bose-Einstein condensates' literature, tends to zero. Moreover, we solve the time-dependent cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearities by using a numerical method.